Emergence of canonical ensembles from pure quantum states

TL;DR

This paper demonstrates that in a weakly interacting quantum system, the subsystem naturally evolves into a canonical ensemble from any initial pure state, supporting the quantum foundation of statistical physics.

Contribution

It shows that generic weak interactions with random phases drive pure states into canonical ensembles, establishing a quantum basis for statistical mechanics.

Findings

Subsystems reach canonical states from arbitrary pure states.

Random phases in interaction Hamiltonian are crucial for typicality.

Results support the quantum foundation of thermodynamics.

Abstract

We consider a system weakly interacting with a bath as a thermodynamic setting to establish a quantum foundation of statistical physics. It is shown that even if the composite system is initially in an arbitrary nonequilibrium pure quantum state, the unitary dynamics of a generic weak interaction almost always drives the subsystem into the canonical ensemble, in the usual sense of typicality. A crucial step is taken by assuming that the matrix elements of the interaction Hamiltonian have random phases, while their amplitudes are left unrestricted.